Wednesday, 14 February 2007

DBT8: Homogeneity is Good

Let's consider a particular opening bid, say 1H. A bidding system will typically require somewhere between 5% and 10% of hands to be opened 1H in first seat. Of course, if you were to choose 5% of hands at random, they wouldn't make a very good 1H bid: we have to choose them so that the opening bid provides useful information to partner. Particularly useful is if all the hands which are opened 1H share a property (or properties) in common, as then partner will be able to make deductions without having to wait for further clarification.

For example, suppose that our 1H bid promised exactly five hearts. Then if partner holds an average hand with four hearts, he can deduce that it is likely to be safe to compete to the three-level in hearts. This is based on the Law of Total Tricks, which admittedly is far from infallible, but is a good guide when you know exactly how many cards your partnership has in the suit.

It is fairly unusual to have a bid which shows exact length in the suit. More common would be a bid which shows five or more hearts. In this case, partner would still be justified in bidding to the three-level on an average hand with four hearts, but now if opener turns out to have more than five hearts there is a fair chance that bidding only to the three-level would be under-competing the hand. Similarly, if the 1H opening could occasionally be only a four-card suit, if responder still bids to the three-level there is a danger that this will be too high. Of course, there are many other factors which affect how high we should be competing, but trump length is very important, and so the more specific the information responder has about suit length, the better his chances of getting the decisions right. This is just part of the obvious general principle that a homogeneous bid - one where all the hands opened with that bid have some property in common - is good for providing information to responder. And the more specific the property is, the better.

Let's think a bit more about this 1H bid showing length in hearts. As mentioned already, in most systems the bid does not show exact length: rather there is a range of possible lengths. In this case, there are two properties of the opening bid which become important:

The minimum length promised by the opening bid; and

The average length promised by the opening bid.

For example, in Acol, where the minimum length for a 1H opening is 4 cards, the average length is close to 5. (I'm deliberately being a bit vague about what I mean by "average", but usually this would be interpreted as the arithmetic mean.) But other systems can have very different numbers - even if you consider only 4-card major systems, there is a lot of variety in how often 1H is opened on a 4-card suit.

This poses a problem for responder. If you are in a position where you have to make a decision without further help from opener, then you will have to decide - do you play opener for the minimum length, or for the average length in hearts? Playing opener for his average length will be right most of the time, but if he turns up with fewer cards than the average there is a danger that the partnership will be too high, or even playing in the wrong denomination. Whereas, if you anticipate opener holding his minimum length, you may very well be under-competing. There is not really any good solution to this, you are forced to hedge your bets.

But this is much more of a problem for some systems than for others. The key is this:

It helps to make the minimum length for your bidsas close to the average length as possible.

This is how you avoid responder's problem of what to play for.

And this explains the big advantage of playing 5-card majors.

5-card suits are much more common than 6-card or longer suits. So when you open 1H or 1S showing 5+ cards, the average length is still close to 5. The distinction between minimum length and average length therefore does not worry responder: he can happily play opener for a 5-card suit. From the point of view of homogeneity, a suit opening which promises 5+ cards is about as good as you can get, short of showing the exact length.

4-card opening bids are much worse in this respect. Assuming that you still open 1H or 1S when the major suit is five cards long, the average length for these opening bids is going to be closer to 5 than 4. This means that responder will find it difficult to judge hands with support for the major. (Of course the corresponding advantage that these systems have is that you get to find major-suit support more often in the first place.)

The worst possible case is if you play 4-card majors, always open your longest suit, and tend to open the lower of two 4-card suits. Then virtually the only time you open 1S on a 4-card suit is when you have precisely 4=3=3=3 shape. Here the average length is over one card more than the minimum length. Indeed, I would hardly say it is a homogeneous bid at all: it basically shows either a 4=3=3=3 hand or 5+ spades, and this is very bad news for responder since the first hand type is not particularly great for playing in spades at all, whereas the second type is excellent for spade contracts. How is he supposed to know what to do with spade support? I hope you would not be so foolish as to play this system - the balanced hands are so rare that it's much better to take them out of 1S somehow and guarantee five cards as the minimum. If you're going to play 4-card majors, you need to open them on four cards as often as you possibly can. This brings the average suit length down much closer to the minimum. This is another good reason why if you are playing a strong NT, it makes sense to open 1H or 1S on minimum hands with a 4-card major even if holding a longer minor.

The same principles apply when we are considering the strength promised by an opening bid, rather than the length. That is, we would ideally like to have a precise description of strength, but if forced to use a relatively wide range, we really want the minimum to be as close to the average as possible. For an opening bid which promises 12+ HCP or thereabouts, this usually happens fairly automatically, since hands with higher HCP values are less frequent. But it doesn't always work that way. For example, if you play a short 1C opening and a weak NT, the 1C opening is very often a "strong NT" hand type. This means that the average strength (perhaps it is more helpful to think of the mode here) is not so close to the minimum. Of course this analysis is rather too simplistic, as there are some definite advantages arising from the "multi-way" nature of this bid - opener is known to have either real clubs or extra strength - but having the most common hands so far away from minimum strength should still be a cause for concern.

3 comments:

An interesting topic. I feel like I should have a lot to say, but everything I can think of is rather complicated and not terribly useful!

I'll settle for this. I think that there are other important things besides the length of partner's suit. Say partner has some spades, you have some spades in a flat hand, and the opponents will jump to 3 or 4 hearts. Which definition will enable you to compete more accurately?

Shortage increases the number of expected tricks in comparison to the LoTT; Heart shortage increases the number of total trumps, so if pard doesn't have a 5 card spade suit you really don't care.

In the former situation, the number of total tricks opposite your 5233 will vary greatly depending whether pard is 4333 or 4162.

That is an extreme example, but I consider the Gemini 1H opening (4+H, denies 4S, if only 4H will be 1444 or have a longer minor) to compare reasonably well against a 5-card 1H opening. The 1D opening (any hand with precisely 4 spades) sometimes leaves a flattish partner with lots of trumps needing to know if you have any shape, but assuming responder has some form of direct raise to ask this, I don't think other systems handle these hands any better.

I agree that it's not exactly "length in hearts" which responder needs to know about, but rather something more like "suitability for playing in hearts". Certainly, if you take out balanced hands with a 4-card suit from your opening bid, then that makes it more suitable.

I would still use length as a first approximation though. The other factors are difficult to quantify because the usefulness of things like side-suit shortage depends a lot on the rest of the hands at the table. For example, if partner has five-card support for you then your shortage is very valuable: if he only has three-card support then it is not. Whereas, length in your main suit is always useful.